Question

ABCD is a rhombus in which AC & BD intersect at O. If AB =13cm and OA = 5cm, find BD.​

Answer 1

Answer:

Let's draw a rhombus (See figure below, I used ms paint for the figure)

We know that the diagonals of a rhombus bisect each at right angles.

Thus, OA=OC, then OC=5cm.

Since all sides of a rhombus are equal, AB=BC=CD=DA=5cm.

Now, in ΔOAD, AD²=OA²+OD²

13²=5²+OD²

OD²=13²-5²

OD²=169-25

OD²=144

OD=√144

OD=12cm.

Again, the diagonals of a rhombus bisect each at right angles. Then OBVIOUSLY BD=2OD

BD=2×12

BD=24cm.

This sum needs practise, never byheart it.

HOPE THIS HELPS :D